Numbers in Chemistry
• Observations –
▫ Qualitative –
 quality of a characteristic
 Ex. Tall, short, cold, etc.
▫ Quantitative –
 Measureable quantity
 Ex. 25 cm, 50 m, 3.27 L
SI Units
• System International
Quantity
Unit
Symbol
Length
Meter
M
Mass
Kilogram
Kg
Time
Second
S
Temperature
Kelvin
K
Volume
Liter
L
Amt of substance
mole
mol
Metric Prefixes
Prefix
Symbol
Meaning
Mega
M
Million
Kilo
K
Thousand
Deci
D
Tenth
Centi
C
Hundredth
Milli
m
Thousandth
Micro
μ
Millionth
Nano
n
Billionth
Pico
p
Trillionth
Critical Thinking
1. How many milligrams in one kilogram?
2. How many meters are in 21.5 km?
3. Is it possible to answer this question: How
many mg are in one km?
4. What is the difference between a Mm and a
mm? Which is larger?
Uncertainty in Measurement
• A measurement always has some degree of
uncertainty.
Scientific Notation
• Used to make very large or very small numbers
easy to handle.
• The Mole!
• 6.02 x 1023 =
602,000,000,000,000,000,000,000
When using Scientific Notation, there are
two kinds of exponents: positive and
negative
Positive Exponent:
2.35 x 108
Negative Exponent:
3.97 x 10-7
When changing scientific notation to
standard notation, the exponent tells
you if you should move the decimal:
With a positive exponent, move the decimal to
the right:
4.08 x 103 = 4 0 8
Don’t forget to fill in your zeroes!
When changing scientific notation to
standard notation, the exponent tells
you if you should move the decimal:
With a negative exponent, move the decimal to
the left:
4.08 x 10-3 =
408
Don’t forget to fill in your zeroes!
An easy way to remember this is:
• If an exponent is positive, the number gets
larger, so move the decimal to the right.
• If an exponent is negative, the number gets
smaller, so move the decimal to the left.
The exponent also tells how many spaces to
move the decimal:
4.08 x 103 = 4 0 8
In this problem, the exponent is +3, so
the decimal moves 3 spaces to the right.
The exponent also tells how many spaces to
move the decimal:
4.08 x 10-3 =
408
In this problem, the exponent is -3, so the
decimal moves 3 spaces to the left.
Try changing these numbers from Scientific
1)
8.41 x 10
Notation
to-7Standard Form
2) 3.215 x 108
Try changing these numbers from Standard Form
to Scientific Notation
1) 25, 310, 000, 000, 000, 000
2) 0.000000003018
When changing from Standard Notation to
Scientific
Notation:
1) First, move
the decimal after the first whole
number:
3258
2) Second, add your multiplication sign and
your base (10).
3 . 2 5 8 x 10
3) Count how many spaces the decimal moved
and this is the exponent.
3 . 2 5 8 x 10 3
3 2
1
Mathematic Operations
and Scientific Notation.
• Multiply – Add Exponents
• Divide – Subtract Exponents
• (4.6 x 1034) (7.9 x10-21)
• 8.4x 10-4/4.1 x 1017
Calculator Operations
•
•
•
•
•
•
Calculators make it easy.
Problem: (1.24 x 1012) (3.31 x 1020)
Type in 1.24 EE 12 x 3.31 EE 20 Enter
Try it!
Problem : 5.4 x 1032/ 7.3 x1014
Type in 5.4 EE 32 / 7.3 EE 14 Enter
Adding or Subtracting
• Make sure the exponents are the same OR use
the EE button!
• 4.25 x 1013 + 2.10 x 1014
• 6.4 x10 -18 – 3 x 10-19
• 3.1 x 10-34 + 2.2 x 10-33
Uncertainty in Measurement
• Different people estimate differently.
• Record all certain numbers and one estimated number.
Significant
Figures
• Numbers recorded in a measurement.
▫ All the certain numbers plus first estimated
number
Significant Figures
Rules for Counting Significant Figures
1. Nonzero integers always count as significant figures.
1457
4 significant figures
Significant Figures
Rules for Counting Significant Figures
2. Zeros
a. Leading zeros - never count
0.0025
2 significant figures
b. Captive zeros - always count
1.008
4 significant figures
c. Trailing zeros - count only if the number is written
with a decimal point
100
1 significant figure
100. 3 significant figures
120.0 4 significant figures
Significant Figures
Rules for Counting Significant Figures
3. Exact numbers - unlimited significant figures
• Not obtained by measurement
• Determined by counting
3 apples
• Determined by definition
1 in. = 2.54 cm
Significant Figures
Significant Figures
Rules for Multiplication and Division
• The number of significant figures in the result is the
same as in the measurement with the smallest number
of significant figures.
Significant Figures
Rules for Addition and Subtraction
• The number of significant figures in the result is the
same as in the measurement with the smallest number
of decimal places.